Regression models for ordinal categorical time series data

Abstract

Regression analysis for multinomial/categorical time series is not adequately discussed in the literature. Furthermore, when categories of a multinomial response at a given time are ordinal, the regression analysis for such ordinal categorical time series becomes more complex. In this paper, we first develop a lag 1 transitional logit probabilities based correlationmodel for the multinomial responses recorded over time. This model is referred to as a multinomial dynamic logits (MDL) model. To accommodate the ordinal nature of the responses we then compute the binary distributions for the cumulative transitional responses with cumulative logits as the binary probabilities. These binary distributions are next used to construct a pseudo likelihood function for inferences for the repeated ordinal multinomial data. More specifically, for the purpose ofmodel fitting, the likelihood estimation is developed for the regression and dynamic dependence parameters involved in the MDL model.